I have a good anecdote for you (true story!)
A friend of mine went through this process about 3 years ago. She applied to 10 schools and received 5 offers. The school where she ended up at put her on a waitlist first. She was #1 on the waitlist for a while. At the end of March she received an offer from that school (T10 by the way).
But the best part of the story is: her cohort consists of 4 students and 3 of them were taken from the waitlist. I think that's a story that should give us hope.